Data-driven scaling parameter discovery and modeling for vortex-induced vibration

The maximum amplitude of vortex-induced vibration (VIV) is a critical indicator for assessing structural safety. While several theoretical models exist to predict this amplitude, they exhibit certain limitations. Popular data-driven approaches, such as deep neural networks, face challenges due to the multi-parametric coupling of VIV and insufficient experimental datasets. To overcome these challenges, a “white-box” scaling parameter VIV modeling approach is proposed that applies symbolic regression twice. First, reduce the dimensionality by deriving a scaling parameter s, defined as the Reynolds number minus the mass-damping coefficient. This parameter effectively collapses the peak amplitude data and represents the low dimensional manifold of VIV. Then, a prediction model is further identified between the vibration peak and the scaling parameter s. The robustness and generalization of this scaling parameter approach are validated. Remarkably, even when trained on limited data, the mathematical expression maintains high accuracy and consistency. However, pure data regression fitting has prediction errors and randomness. Finally, the physical interpretation of scaling parameter is linked to the energy competition between fluid and structure, offering physical insight into the underlying mechanism.